Model analysis of electrical conduction through morphologically complex cells and cell masses

Abstract

Examination of fundamental field theory relevant to the distribution of electrical conduction at low frequencies and intensities through passive tissues composed of thin membranes in volume electrolytes indicates that structurally similar inanimate models can also be made electrodynamically similar, regardless of morphological complexity, simply by matching values of “membrane number” (a non-dimensional function of normal membrane resistivity, electrolyte conductivity, and size) everywhere in model and tissue. Metallic electrolytic-tank models of simple cell shapes have in the past occasionally been formed using various conventional construction methods and may still have value, especially in light of a more quantitative theory of electrical modeling. But, at least for the investigation of tissue impedance factors, far more realistic (and steadily improving) structural models of single, profusely branching and interwoven brain cells and laminar neuronal arrays can be “grown” by sequential dendritic electrodeposition of one or more metals from solution. These electrodeposition processes can then be followed by total immersion in acid to form a uniform and reproducible high-resistance passive surface layer on those parts of the model intended to represent high-resistance cell membranes. An ample variety of experimental process controls exist and are being explored together with an examination of approximations and “don't-care” conditions which will facilitate the modeling of aggregates of such small cells in a practical experimental sense. The most useful allowable deviation from exact theory in the investigation of impedance factors (involving, therefore, only external energy sources or power supply) concerns the model materials and conductivity corresponding to intracellular fluid: in such problems, due to the relatively high resistance of cell membranes, very little current flows through the cells and, furthermore, most of the energy loss in whatever transcellular charge transfer does occur takes place just at the cell walls. Hence, solid-metal cell models (such as electrodeposited dendrites) may be used for convenience in this case with very small error, even though such model cells have substantially higher internal conductivity (and even lower relative energy loss) than that called for by exact theory.